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    • adjusted the formatting of the formulas a little, for readability. While I was at it, I added a one-sentence Idea-section, for completeness.

      diff, v10, current

    • Page created, but author did not leave any comments.

      v1, current

    • I corrected a couple og microscopic typos at k-ary factorization system, and then I noticed that something is unclear in the definition: first of all the family of factorization system is asked to be strong (= uniqueness of solution to any lifting problem) or weak (existence, no uniqueness)? And when the definition says

      M 1⊆…⊆M κ−1M_1 \subseteq \dots \subseteq M_{\kappa-1} whenever this is meaningful (equivalently, E k−1⊆…⊆E 1E_{k-1} \subseteq\dots\subseteq E_{1})

      what does it precisely mean? Are we asking that right classes be nested?

      Thirdly, it is my humble opinion that saying

      A discrete category has a (necessarily unique) (−1)(-1)-ary factorisation system.

      is formally incorrect: discrete categories are groupoids where the only arrows are identities, so this is a particular kind of 0-ary factorization system.

      Instead, negative thinking suggests that (-1)-ary factorization systems live in non-unital categories, and detect precisely the case where the class of isomorphisms is empty (recall that in a WFS (L,R)(L,R) the intersection L∩RL\cap R consists of all isomorphisms; if in a 0-ary factorization system we had L=R=L∩R=Iso(C)L=R=L\cap R=Iso(\mathbf C), morally in a (-1)-ary system the intersection has to be empty, giving a category without identities -i.e. a particular kind of “plot”, in the jargon of this paper which I finally convinced my friend Salvatore to put on the arXiv-, and more precisely an associative, “strongly nonunital” plot).

      This leads to another question: how can be the notion of (W)FS be extended to Mitchell’s semicategories (with empty or partially defined identity function)?

    • I added a bit to the section on the ultrafilter monad in ultrafilter. This could stand to be fleshed out still more. The immediate reason for my editing here was to put down the notion of “compact Hausdorff object” (which is used in a remark at BoolAlg).

    • Page created, but author did not leave any comments.

      v1, current

    • Kochmann should be Kochman: https://bookstore.ams.org/fim-7

      Presumably #Kochmann96 should be corrected to #Kochman96, but I haven’t changed this as I’m afraid I might break things.

      Anonymous

      diff, v34, current

    • Page created, but author did not leave any comments.

      v1, current

    • Page created, but author did not leave any comments.

      v1, current

    • As written, I do not believe Theorem 4.1 is true. Certainly, the coreflection exists but it is unclear why the topology generated by the connected components of the open subsets of XX is in fact a locally connected space. It is only obvious that locally connected spaces are the fixed points of this construction. Either this case was being mistaken for the locally path-connected case or the mistake was made of assuming that connected subspaces of XX still need to be connected as subspaces of R(X)R(X). Looking at the literature (Gleason’s paper “Universally locally connected refinements”) this simple refinement is used to show that the coreflection exists. However, the simple refinement and coreflection don’t seem to be the same. Rather, the coreflection is only guaranteed to be the infimum (in the lattice of topologies) of locally connected topologies larger than the topology of XX.

      Jeremy Brazas

      diff, v7, current

    • Someone anonymous has noted that the labels in two diagrams in triangle identities are misplaced. This seems clear. As the diagrams are external, can someone edit them who has access to the original code? There seem to be other errors (e.g. a C should be a D), as well.

    • a stub, for the moment just to make links work

      v1, current

    • starting something on Ravenel’s spectra X(n)X(n). Nothing to be seen yet, but I need to save…

      v1, current

    • wrote out parts of the proof of Ω • un≃π •MO\Omega^{un}_\bullet \simeq \pi_\bullet M O at Thom spectrum

    • Add basic definition in context of algebraic topology. My first contribution.

      Grant

      diff, v5, current

    • Weakly reductive semigroups is a special class of semigroups that include monoids and is interesting from the perspective of being able to represent a semigroup as its translations.

      Adam

      v1, current

    • Page created, but author did not leave any comments.

      v1, current

    • starting something – not done yet

      v1, current

    • Today I was asked for what I know about the development of the theory of Kan-fibrant simplicial manifolds. I realized that the nLab does not discuss this, so I have started a page now with the facts that come to mind right away. (Likely I forgot various things that should still be added.)

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • The conjecture is not true for all single-sorted algebraic theories and this was known by Soviet mathematicians. I added a short high-level explanation on this and some references to translated works that have more detail. Presumably one should edit rest of the page (and references to it) to make it clear throughout that (i) the conjecture is false (ii) the general question “Which algebraic categories have the Higman property?” is still interesting (and potentially something category-theorists could study).

      diff, v6, current

    • Edited the section on Boone conjecture in light of it being false.

      diff, v9, current

    • page about algebraic compactness.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • https://math.stackexchange.com/a/100521/476484 contains all the necessary references

      Anonymous

      v1, current

    • I added some stuff about the connection between Riccati equations and the projective linear group, which seems to explain the point of these equations.

      diff, v3, current

    • I am giving this its own little entry, for ease of collecting some facts and resources…

      …such as the MO discussions (MO:a/44885/381, MO:a/218053/381) on how K3∖24S 3K3 \setminus 24 S^3 is the cobordism that witnesses 24[S 3]=0∈Ω 3 fr24 [S^3] = 0 \in \Omega^{fr}_3. There must be a more citeable reference for this, though. If anyone has the pointer, let’s add it.

      v1, current

    • a stub, to record some references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have touched the Examples-section at sequentially compact topological space:

      1. moved the detailed discussion of the compact space {0,1} [0,1]\{0,1\}^{[0,1]} which is not sequ compact to the examples-section at compact topological space, and left a pointer to it,

      2. added pointers (just pointers for the moment) to two detailed discussions of examples of sequ compact spaces that are not compact.

    • needed to be able to point to duality in physics, so I created an entry. For the moment just a glorified redirect.

    • brief category:people-entry for hyperlinking references

      v1, current

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